Question

Find the values of k and b if it is known that the graph of y=kx b goes through points (2, 10) and (−7, −10).

Answer 1

The values of k and b of this graph that passes through the given points is $k = \frac{20}{9}$  and $b = \frac{-50}{9}$

Given the following points:

• Points on the x-axis = (2, -7)

• Points on the y-axis = (10, -10)

• $y = kx + b$   .....equation 1.

To find the values of k and b since the graph passes through the given points:

First of all, we would determine the slope of the graph passing through the given points.

$Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points into the formula, we have;

$Slope. \;m = \frac{-10 - 10}{-7 - 2}\\\\Slope. \;m = \frac{-20}{-9}\\\\Slope. \;m = \frac{20}{9}$

The standard form of an equation of line is given by the formula;

$y = mx + b$   ....equation 2

Where:

• x and y are the points.

• m is the slope.

• b is the intercept.

Next, we would determine the intercept of the graph:

$10 = \frac{20}{9}(2) + b\\\\10 = \frac{40}{9} + b\\\\b = \frac{40}{9} - 10\\\\b = \frac{40\; - \;90}{9}\\\\b = \frac{-50}{9}$

The standard form of this equation of line is:

$y = \frac{20}{9}x - \frac{50}{9}$    .....equation 3.

Comparing eqn 1 and eqn 3, we can deduce:

$k = \frac{20}{9}$  and $b = \frac{-50}{9}$

Therefore, the values of k and b of this graph that passes through the given points is $k = \frac{20}{9}$  and $b = \frac{-50}{9}$

Read more: brainly.com/question/18123312